General Instructions s6

Fall 10 EEE-161 10-20-10 Midterm General instructions: . 10/20/10 Wednesday, 6:00 to 7:15 pm, RVR-1006 . Open book/note . Use engineering units . 5 problems – 20 points each . No computer (laptop, palmtop, …) . Show your work. Just an answer, even if it is the right one, is not good enough. . You need to include units in your answer.

1) A short-circuited 75-ohm transmission line (r = 1) is used to replicate the effect of a 5 pF capacitor at 3 GHz. Determine the shortest possible length of this line.

2) A 50- ideal transmission line (r = 4) carrying a 1.5 GHz signal is terminated with

ZL = 50  – j35 . a) Find the reflection coefficient  (in polar form) and VSWR. b) Find the input impedance Zin (in rectangular form) 6 cm away from ZL. 3) Determine the Electric field (in rectangular coordinates) @ (4,-5,6) due to a point charges: Q = 5 nC @ (1,2,-3). 4) Determine the Electric field (in rectangular coordinates) @ (0,2,3) due to the following point charges: Q1 = 10 pC @ (0,0,0), Q2 = -5 pC @ (0,1,0), and Q3 = 15 pC @ (0,1,-1). 5) Determine the Electric field (in cylindrical coordinates) at point P if the line charge

carries a uniform density l = 20 pC/m and d = 2 m. z d d

6) A point charge of 100 pC is at the center of a thin spherical shell with radius = 3 m 2 and surface charge density s = -5 pC/m . Determine the E-field at r = 2 m and 4 m.

7) An infinitely long cylinder with radius = 2 cm and volume charge density v = 6 3 2 C/m is surrounded by a concentric thin cylindrical shell with s = 0.02 C/m and radius = 4 cm. Determine the E-field at r = 1 cm, 3 cm, and 5 cm. 8) Determine the potential if a test charge is moved from (0,5,1) to (0,2,3) and given that the electric field components are: -2z Ex = 0, Ey = 0, and Ez = 2 e . 2,3,5,6,8 Fall 10 EEE-161 10-20-10 Midterm

c 8 m 1) f  3GHz   1 v  v  3  10 Z  75 r s 0 r 1 0 C  5 pF X  X  10.61 10  C 2 f C C

v 360deg 3 deg     0.1m     3.6  10 f  m

1   1   3 l    atan  l  47.763 10 m    2. f C Z0 

c 8 m 2) f  1.5GHz   4 v  v  1.5  10 Z  50 Z  50  j35 r s 0 L r ZL  Z0     0.109  0.312i   0.33 arg()  70.71 deg ZL  Z0

1   VSWR  VSWR  1.987 1  

v 360deg 3 deg     0.1 m     3.6  10 L  6cm  L  216 deg f  m

ZLcos L  jZ0sin L Zin  Z0 Zin  27.248  12.243i Z0cos L  jZLsin L

3) Q1  5nC

Q1x  1m QPx  4m

Q1y  2m QPy  5m

Q1z  3m QPz  6m

2 2 2 R1x  QPx  Q1x R1y  QPy  Q1y R1z  QPz  Q1z R1  R1x  R1y  R1z R1  11.79m

 R   R   R  Q1  1x  V Q1  1y  V Q1  1z  V E1x  E1x  0.082 E1y  E1y  0.192 E1z  E1z  0.247 4   3  m 4   3  m 4   3  m 0  R1  0  R1  0  R1  Fall 10 EEE-161 10-20-10 Midterm

4) Q1  10 pC Q2  5 pC Q3  15 pC

Q1x  0m Q2x  0m Q3x  0m QPx  0m

Q1y  0m Q2y  1m Q3y  1m QPy  2m

Q1z  0m Q2z  0m Q3z  1m QPz  3m

2 2 2 R1x  QPx  Q1x R1y  QPy  Q1y R1z  QPz  Q1z R1  R1x  R1y  R1z R1  3.606 m

 R   R   R  Q1  1x  V Q1  1y   3 V Q1  1z   3 V E1x  E1x  0 E1y  E1y  3.835  10 E1z  E1z  5.753  10 4   3  m 4   3  m 4   3  m 0  R1  0  R1  0  R1   R   R   R  Q2  2x  V Q2  2y   3 V Q2  2z   3 V E2x  E2x  0 E2y  E2y  1.421  10 E2z  E2z  4.263  10 4   3  m 4   3  m 4   3  m 0  R2  0  R2  0  R2   R   R   R  Q3  3x  V Q3  3y   3 V Q3  3z   3 V E3x  E3x  0 E3y  E3y  1.923  10 E3z  E3z  7.694  10 4   3  m 4   3  m 4   3  m 0  R3  0  R3  0  R3  V E  E  E  E E  0 x 1x 2x 3x x m

 3 V E  E  E  E E  4.337  10 y 1y 2y 3y y m

 3 V E  E  E  E E  9.183  10 z 1z 2z 3z z m

pC 5) z  2m z  4m   20 a  0m 1 2 l m

V l  1 1  V Er  0 Ez     Ez  0.045 m 4 0  2 2 2 2  m  a  z2 a  z1 

100pC  3 V 6) r  2m E  E  224.694 10 r 2 r m 4 0r pC 2 5 4 (3m) 2 100pC m  3 V r  4m E   E  261.48 10 r 2 2 r m 4 0r 4 0r Fall 10 EEE-161 10-20-10 Midterm

C 2 7) r  1cm   6 Q   r L S 2 rL v 3 v m 2 v  r 3 V Er  Er  3.388 10 2 0 r m

C 2 r  3cm   6 Q   (2cm) L S 2 rL v 3 v m 2 v  (2cm) 3 V Er  Er  4.518 10 2 0 r m

C 2 r  5cm   6 Q1   (2cm) L S 2 rL v 3 v m 2 v  (2cm) 3 V Er1  Er1  2.711 10 2 0 r m

C s2 4cm 3 V   0.02 E  E  1.807 10 s 2 r2 r2 m m 2 0 r

 2z 8) Ez( z)  2e P1 (1 5 1) P2 (3 2 3)

3    E ( z) d z  0.133  E ( z) d z  exp (2z)  z  z   1